Category:Inductive Sets

This category contains results about Inductive Sets.

Then $S$ is inductive if and only if:

$(1)$	$:$	$S$ contains the empty set:		$\ds \quad \O \in S $
$(2)$	$:$	$S$ is closed under the successor mapping:	$\ds \forall x:$	$\ds \paren {x \in S \implies x^+ \in S} $	where $x^+$ is the successor of $x$
					That is, where $x^+ = x \cup \set x$

Subcategories

This category has the following 2 subcategories, out of 2 total.

The following 5 pages are in this category, out of 5 total.

\((1)\)	$:$	$S$ contains the empty set:		\(\ds \quad \O \in S \)
\((2)\)	$:$	$S$ is closed under the successor mapping:	\(\ds \forall x:\)	\(\ds \paren {x \in S \implies x^+ \in S} \)	where $x^+$ is the successor of $x$
					That is, where $x^+ = x \cup \set x$